Massimo Franchi, Paolo Paruolo
arXiv 20 Dec 2017 · Econometrics
arXiv:1712.07522 · PDF · DOI · OpenAlex · Extracted main text
This paper defines the class of $\mathcal{H}$-valued autoregressive (AR) processes with a unit root of finite type, where $\mathcal{H}$ is an infinite dimensional separable Hilbert space, and derives a generalization of the Granger-Johansen Representation Theorem valid for any integration order $d=1,2,\dots$. An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer $d$ and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and $(i)$ the order of integration, $(ii)$ the structure of the attractor space and the cointegrating space, $(iii)$ the expression of the cointegrating relations, and $(iv)$ the Triangular representation of the process. Except for the fact that the number of cointegrating relations that are integrated of order 0 is infinite, the representation of $\mathcal{H}$-valued ARs with a unit root of finite type coincides with that of usual finite dimensional VARs, which corresponds to the special case $\mathcal{H}=\mathbb{R}^p$.
appendix boundary found by appendix_command · 67% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Beare, B. and W. Seo (2018) Representation of I(1) and I(2) autoregressive Hilbertian processes | 1.000 | 9 | 4 | 100% |
| 2 | Beare, B., J. Seo, and W. Seo (2017) Cointegrated Linear Processes in Hilbert Space | 1.000 | 9 | 4 | 100% |
| 3 | Chang, Y., C. Kim, and J. Park (2016) Nonstationarity in time series of state densities | 1.000 | 9 | 3 | 100% |
| 4 | Johansen, S (1996) Likelihood-based Inference in Cointegrated Vector Auto-Regressive Models | 1.000 | 9 | 3 | 100% |
| 5 | Hu, B. and J. Park (2016) Econometric Analysis of Functional Dynamics in the Presence of Persistence | 1.000 | 8 | 5 | 100% |
| 6 | Bosq, D (2000) Linear Processes in Function Spaces | 0.928 | 5 | 4 | 80% |
| 7 | Franchi, M. and P. Paruolo (2018) A general inversion theorem for cointegration self | 0.874 | 6 | 3 | 67% |
| 8 | Chang, Y., B. Hu, and J. Park (2016) On the Error Correction Model for Functional Time Series with Unit Roots | 0.843 | 3 | 3 | 100% |
| 9 | Gohberg, I., S. Goldberg, and M. Kaashoek (1990) Classes of linear operators, vol. 1 | 0.830 | 7 | 3 | 57% |
| 10 | Gohberg, I., S. Goldberg, and M. Kaashoek (2003) Basic Classes of Linear Operators | 0.763 | 9 | 4 | 44% |
Showing the top 10 of 68 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Representation of I(1) and I(2) autoregressive Hilbertian processes | 1.000 | 6 | 3 |
| 2 | 1cm Inference on common trends in functional time series | 0.644 | 2 | 2 |
| 3 | 2102.10626 | 0.405 | 1 | 1 |
| 4 | The general solution to an autoregressive law of motion | 0.405 | 1 | 1 |
| 5 | Large-Scale Curve Time Series with Common Stochastic Trends | 0.405 | 1 | 1 |
| 6 | Canonical correlation analysis of stochastic trends via functional approximation | 0.000 | 1 | 1 |